1,541 research outputs found
A Unified Framework for Sparse Non-Negative Least Squares using Multiplicative Updates and the Non-Negative Matrix Factorization Problem
We study the sparse non-negative least squares (S-NNLS) problem. S-NNLS
occurs naturally in a wide variety of applications where an unknown,
non-negative quantity must be recovered from linear measurements. We present a
unified framework for S-NNLS based on a rectified power exponential scale
mixture prior on the sparse codes. We show that the proposed framework
encompasses a large class of S-NNLS algorithms and provide a computationally
efficient inference procedure based on multiplicative update rules. Such update
rules are convenient for solving large sets of S-NNLS problems simultaneously,
which is required in contexts like sparse non-negative matrix factorization
(S-NMF). We provide theoretical justification for the proposed approach by
showing that the local minima of the objective function being optimized are
sparse and the S-NNLS algorithms presented are guaranteed to converge to a set
of stationary points of the objective function. We then extend our framework to
S-NMF, showing that our framework leads to many well known S-NMF algorithms
under specific choices of prior and providing a guarantee that a popular
subclass of the proposed algorithms converges to a set of stationary points of
the objective function. Finally, we study the performance of the proposed
approaches on synthetic and real-world data.Comment: To appear in Signal Processin
A Perceptual Evaluation of Short-Time Fourier Transform Window Duration and Divergence Cost Function on Audio Source Separation using Non-negative Matrix Factorization
Non-negative matrix factorization (NMF) is an established method of performing audio source separation. Previous studies used NMF with supplementary systems to improve performance, but little has been done to investigate perceptual effects of NMF parameters. The present study aimed to evaluate two NMF parameters for speech enhancement: the short-time Fourier transform (STFT) window duration and divergence cost function. Two experiments were conducted: the first investigated the effect of STFT window duration on target speech intelligibility in a sentence keyword identification task. The second experiment had participants rate residual noise levels present in target speech using three different cost functions: the Euclidian Distance (EU), the Kullback-Leibler (KL) divergence, and the Itakura-Saito (IS) divergence. It was found that a 92.9 ms window duration produced the highest intelligibility scores, while the IS divergence produced significantly lower residual noise levels than the EU and KL divergences. Additionally, significant positive correlations were found between subjective residual noise scores and objective metrics from the Blind Source Separation (BSS_Eval) and Perceptual Evaluation method for Audio Source Separation (PEASS) toolboxes. Results suggest longer window durations, with increased frequency resolution, allow more accurate distinction between sources, improving intelligibility scores. Additionally, the IS divergence is able to more accurately approximate high frequency and transient components of audio, increasing separation of speech and noise. Correlation results suggest that using full bandwidth stimuli could increase reliability of objective measures
An investigation of the utility of monaural sound source separation via nonnegative matrix factorization applied to acoustic echo and reverberation mitigation for hands-free telephony
In this thesis we investigate the applicability and utility of Monaural Sound Source Separation (MSSS) via Nonnegative Matrix Factorization (NMF) for various problems related to audio for hands-free telephony. We first investigate MSSS via NMF as an alternative acoustic echo reduction approach to existing approaches such as Acoustic Echo Cancellation (AEC). To this end, we present the single-channel acoustic echo problem as an MSSS problem, in which the objective is to extract the users signal from a mixture also containing acoustic echo and noise. To perform separation, NMF is used to decompose the near-end microphone signal onto the union of two nonnegative bases in the magnitude Short Time Fourier Transform domain. One of these bases is for the spectral energy of the acoustic echo signal, and is formed from the in- coming far-end user’s speech, while the other basis is for the spectral energy of the near-end speaker, and is trained with speech data a priori. In comparison to AEC, the speaker extraction approach obviates Double-Talk Detection (DTD), and is demonstrated to attain its maximal echo mitigation performance immediately upon initiation and to maintain that performance during and after room changes for similar computational requirements. Speaker extraction is also shown to introduce distortion of the near-end speech signal during double-talk, which is quantified by means of a speech distortion measure and compared to that of AEC. Subsequently, we address Double-Talk Detection (DTD) for block-based AEC algorithms. We propose a novel block-based DTD algorithm that uses the available signals and the estimate of the echo signal that is produced by NMF-based speaker extraction to compute a suitably normalized correlation-based decision variable, which is compared to a fixed threshold to decide on doubletalk. Using a standard evaluation technique, the proposed algorithm is shown to have comparable detection performance to an existing conventional block-based DTD algorithm. It is also demonstrated to inherit the room change insensitivity of speaker extraction, with the proposed DTD algorithm generating minimal false doubletalk indications upon initiation and in response to room changes in comparison to the existing conventional DTD. We also show that this property allows its paired AEC to converge at a rate close to the optimum. Another focus of this thesis is the problem of inverting a single measurement of a non- minimum phase Room Impulse Response (RIR). We describe the process by which percep- tually detrimental all-pass phase distortion arises in reverberant speech filtered by the inverse of the minimum phase component of the RIR; in short, such distortion arises from inverting the magnitude response of the high-Q maximum phase zeros of the RIR. We then propose two novel partial inversion schemes that precisely mitigate this distortion. One of these schemes employs NMF-based MSSS to separate the all-pass phase distortion from the target speech in the magnitude STFT domain, while the other approach modifies the inverse minimum phase filter such that the magnitude response of the maximum phase zeros of the RIR is not fully compensated. Subjective listening tests reveal that the proposed schemes generally produce better quality output speech than a comparable inversion technique
An investigation of the utility of monaural sound source separation via nonnegative matrix factorization applied to acoustic echo and reverberation mitigation for hands-free telephony
In this thesis we investigate the applicability and utility of Monaural Sound Source Separation (MSSS) via Nonnegative Matrix Factorization (NMF) for various problems related to audio for hands-free telephony. We first investigate MSSS via NMF as an alternative acoustic echo reduction approach to existing approaches such as Acoustic Echo Cancellation (AEC). To this end, we present the single-channel acoustic echo problem as an MSSS problem, in which the objective is to extract the users signal from a mixture also containing acoustic echo and noise. To perform separation, NMF is used to decompose the near-end microphone signal onto the union of two nonnegative bases in the magnitude Short Time Fourier Transform domain. One of these bases is for the spectral energy of the acoustic echo signal, and is formed from the in- coming far-end user’s speech, while the other basis is for the spectral energy of the near-end speaker, and is trained with speech data a priori. In comparison to AEC, the speaker extraction approach obviates Double-Talk Detection (DTD), and is demonstrated to attain its maximal echo mitigation performance immediately upon initiation and to maintain that performance during and after room changes for similar computational requirements. Speaker extraction is also shown to introduce distortion of the near-end speech signal during double-talk, which is quantified by means of a speech distortion measure and compared to that of AEC. Subsequently, we address Double-Talk Detection (DTD) for block-based AEC algorithms. We propose a novel block-based DTD algorithm that uses the available signals and the estimate of the echo signal that is produced by NMF-based speaker extraction to compute a suitably normalized correlation-based decision variable, which is compared to a fixed threshold to decide on doubletalk. Using a standard evaluation technique, the proposed algorithm is shown to have comparable detection performance to an existing conventional block-based DTD algorithm. It is also demonstrated to inherit the room change insensitivity of speaker extraction, with the proposed DTD algorithm generating minimal false doubletalk indications upon initiation and in response to room changes in comparison to the existing conventional DTD. We also show that this property allows its paired AEC to converge at a rate close to the optimum. Another focus of this thesis is the problem of inverting a single measurement of a non- minimum phase Room Impulse Response (RIR). We describe the process by which percep- tually detrimental all-pass phase distortion arises in reverberant speech filtered by the inverse of the minimum phase component of the RIR; in short, such distortion arises from inverting the magnitude response of the high-Q maximum phase zeros of the RIR. We then propose two novel partial inversion schemes that precisely mitigate this distortion. One of these schemes employs NMF-based MSSS to separate the all-pass phase distortion from the target speech in the magnitude STFT domain, while the other approach modifies the inverse minimum phase filter such that the magnitude response of the maximum phase zeros of the RIR is not fully compensated. Subjective listening tests reveal that the proposed schemes generally produce better quality output speech than a comparable inversion technique
Statistical single channel source separation
PhD ThesisSingle channel source separation (SCSS) principally is one of the challenging fields
in signal processing and has various significant applications. Unlike conventional
SCSS methods which were based on linear instantaneous model, this research sets out
to investigate the separation of single channel in two types of mixture which is
nonlinear instantaneous mixture and linear convolutive mixture. For the nonlinear
SCSS in instantaneous mixture, this research proposes a novel solution based on a
two-stage process that consists of a Gaussianization transform which efficiently
compensates for the nonlinear distortion follow by a maximum likelihood estimator to
perform source separation. For linear SCSS in convolutive mixture, this research
proposes new methods based on nonnegative matrix factorization which decomposes a
mixture into two-dimensional convolution factor matrices that represent the spectral
basis and temporal code. The proposed factorization considers the convolutive mixing
in the decomposition by introducing frequency constrained parameters in the model.
The method aims to separate the mixture into its constituent spectral-temporal source
components while alleviating the effect of convolutive mixing. In addition, family of
Itakura-Saito divergence has been developed as a cost function which brings the
beneficial property of scale-invariant. Two new statistical techniques are proposed,
namely, Expectation-Maximisation (EM) based algorithm framework which
maximizes the log-likelihood of a mixed signals, and the maximum a posteriori
approach which maximises the joint probability of a mixed signal using multiplicative
update rules. To further improve this research work, a novel method that incorporates
adaptive sparseness into the solution has been proposed to resolve the ambiguity and
hence, improve the algorithm performance. The theoretical foundation of the proposed
solutions has been rigorously developed and discussed in details. Results have
concretely shown the effectiveness of all the proposed algorithms presented in this
thesis in separating the mixed signals in single channel and have outperformed others
available methods.Universiti Teknikal Malaysia Melaka(UTeM),
Ministry of Higher Education of Malaysi
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